Variability of molecular biomarker measurements from nonlinear calibration curves

In any immunoassay experiment for the detection of molecular biomarkers, a nonlinear calibration curve is constructed to relate fixed biomarker concentrations to observed tracer levels. The biomarker concentration in an experimental sample can then be estimated by projecting the experimental tracer measurements through the inverse of the calibration curve. Once an estimate of the biomarker level has been calculated, it is often of interest to determine its variability. Typically, methods for estimating this variability assume that the biomarker variability is due solely to the uncertainty in the estimation of the calibration curve. A more complete analysis would combine this uncertainty with the variability in the processing and measurements of the sample, including, e.g., measurement error of laboratory procedures or variation in enzymatic activity in enzyme-linked immunosorbent assays or radioactivity counts in RIAs. In this paper, we present a method of estimating the variability of inverse estimates assuming there is variation arising from both the determination of the calibration curve and from the preparation and measurement of the experimental sample. Our method uses a resampling algorithm that avoids requiring many distributional assumptions present in alternative procedures, can be easily implemented, and is generalizable to any immunoassay procedure. Methods for incorporating our results in the estimation of variability for planning and analyzing biomarker experiments are discussed. We provide an example using RIA data for aflatoxin B1 detection. These biomarkers for aflatoxin exposure are used in the analysis of serum aflatoxin adduct levels in human and experimental samples, and they are important in hepatocellular carcinoma research.